China does have a functioning democracy. Looking at polling, the large majority in China believe the state represents their interests, and is in fact democratic:

The Chinese political system is based on whole-process people's democracy, a form of consultative democracy. The local government is directly elected, and then these governments elect people to higher rungs, meaning any candidate at the top level must have worked their way up from the bottom and directly proved themselves. Moreover, the economy in the PRC is socialist, with public ownership as the principle aspect of the economy. Combining this consultative, ground-up democracy with top-down economic planning is the key to China's success.

I highly recommend Roland Boer's Socialism in Power: On the History and Theory of Socialist Governance. Socialist democracy has been imperfect, but has gone through a number of changes and adaptations over the years as we've learned more from testing theory to practice. Boer goes over the history behind socialist democracy in this textbook.